\(Q^\pi _{cpt}(s,a)\)  will be bounded when \(|r(s,a)| < \infty \)  and \(\gamma \in (0,1)\) .
In reinforcement learning, transition probabilities and rewards are typically not known apriori.
In the absence of a model, the agent will have to estimate \(Q^\pi _{cpt}(s,a)\)  and learn `good' policies by exploring its environment.
Since \(Q^\pi _{cpt}(s,a)\)  is evaluated for each action in a state, this quantity can be estimated without knowledge of the transition probabilities.
This is in contrast to [1]}, where a model of the system was assumed to be available, and costs were known.
